Why Study Algebra?

[AZTheta]

Hey MysticCat! check this out and tell me what you think. I know nothing about it but can vouch for the person who referred me to it. I'll come back and post the isbn here as soon as she sends it to me.

Visual Mathematics: A Step by Step Guide (title is what she quoted, so best to wait for the isbn, right?)

[ThetaPrincess24]

Originally Posted by MysticCat

And to be clear, obviously I know there are many professions and occupations where you would need to know higher forms of math. But I think he's like me: I knew I disliked math enough that any career that required lots of it was automatically excluded from consideration. I guess what I'm looking for are examples from anyone not in a math-oriented field as to how they've used what they learned in algebra.

When I was in nursing, I used basic ratio/proportion algebra to figure out medication dosages nearly everyday while at the hospital. But that was about the only time I used it. Higher forms of math was never used.

I'm still trying to figure out why elementary calculus & finite math was necessary for me to complete my business degree. A lot of economics, accounting, & finance formulas come out of calculus, but one does not need to know how to do calculus to find the answers, just basic algebra. Even then in the real world, computer programs run those formulas for you. I saw some of the finite math stuff in my statistics class, but outside of that I've never seen it again.

[melindawarren]

Ok, I win at worst HS math situation (I remember a board of education member once saying to me, "you never did quite have luck with math classes, did you?"). But I still see the value to a basic understanding of algebra. I can't think of anything specific that algebra taught me that, say, basic math didn't (especially because I somehow managed to get myself into a math class in my junior year called "Finite Math." It was basic math all the way to introductory algebra. We only got to do it that way because the first semester was statistics. I don't know how this managed to come after Algebra II, but it was SOOO cool that it did!), but I can say that, imo, some of these annoying classes (things like Algebra or World History) just teach useful skills.

My math classes taught me that some problems only one answer. They taught me how to collaborate with classmates when a particular teacher was being unreasonable, they taught me how to verbalize my concerns over a grade (with a less tangible subject like, say, English, where an essay is incredibly subjective, math tends to be more objective, and if a teacher marked an answer wrong but it was clearly right, you can easily win that one!), and how to attack one challenge multiple ways (because algebra is that kind of subject: there is [usually] only one answer, but there are [usually] multiple paths to that one answer).

Personally? I still hate math, and I avoid using anything beyond basic math when I can. Nonetheless, I still love solving ratios, calculating my grades with fancy formulas, and the occasional multiplication/division question. But algebra? I hardly remember it-I just remember that I learned about things other than math in my high school math classes.

[preciousjeni]

I use algebra on a regular basis, especially to figure out complex percentages. I have trouble visualizing where the numbers go in the equation, so I'll write an equation fully out and then do the calculations in my head.

People use basic algebra all the time without thinking about it. Once you have the concepts in mind, you forget that it's "algebra" and you just think of it as working out an equation.

[MysticCat]

Originally Posted by AlwaysSAI

I currently teach Algebra I in the same state you live, MC, and in a county not very far away. Let me know if you decide you want an algebra tutor. (;

This is very true and in the state you live, it is a result of standardized testing. There are "more creative" things that can be done with Algebra but because Algebra I is and always will be an EOC class, teachers are less likely to do more fun things. Their goal is to teach it exactly how it will look on the EOC so that the students can pass it. (As an special ed teacher teaching Algebra, my approach is a bit different, but gets the same result.)

This is certainly part of the problem, but I came along long before teaching for the test, and it was a problem then as well. Teaching for the test exacerbates the problem, I think.

And thanks for the tutoring offer. We actually have a really great tutor and who is making some good progress. She's a friend whose family he's known all his life, and she has a son a year older than ours with similar spectrum challenges, so she has a really good sense of how to approach things with him. She is seeing promise.

Originally Posted by psusue

The other point I have is that he has no idea yet what will truly interest him-- many of the topics that he may go on to love haven't yet been covered.

Exactly! We keep reminding him of this, along with the basic "you need this to get into college to study what you want to study." Your whole post was very helpful and encouraging. Thanks!

Originally Posted by southbymidwest

MysticCat, I think your son has to look at this at a macro versus micro level also. School is about learning about all sorts of stuff, even that which you don't have an affinity for, or like. I'd bet big money that the vast majority of us took classes in something that we despised, and thought that they were "stupid" to take.

He definitely does need to look at it this way, and we hit on this every time we talk about algebra. The challenge is that when you're talking about a 14-year-old with Asperger's, getting him to that macro-perspective is a lot easier said than done.


Thanks everyone for the suggestions. There's so much that I don't think that I can respond to everything everyone has said, but I really appreciate it all!


ETA:

Originally Posted by psusue

For example, I HATED math with the burning passion of a thousand fiery suns . . . .

I meant to give psusue major props for this reference.

[sigmagirl2000]

linear equations can be used in simple applications like "I have to pay my cell phone bill. It costs $50 a month, then $.10 for every text I go over however many are allotted in the plan." The .10 would be your slope, and the $50 would be your y-intercept. You can use those to graph and determine how much you will pay per month based on the number of texts over your plan you use, etc. You can compare your own cell phone plan to other plans to determine if you have the best plan based on your usage and needs (by solving a system of equations.) etc. I don't know. As a math teacher, I constantly apply what we are doing in classes to teens.... if you want more ways, let me know and I'll pay attention to the things that fall out of my mouth during class when I get "why do we need this?" questions. (because the responses are spontaneous, and without any thought)

[southbymidwest]

Originally Posted by sigmagirl2000

linear equations can be used in simple applications like "I have to pay my cell phone bill. It costs $50 a month, then $.10 for every text I go over however many are allotted in the plan." The .10 would be your slope, and the $50 would be your y-intercept. You can use those to graph and determine how much you will pay per month based on the number of texts over your plan you use, etc. You can compare your own cell phone plan to other plans to determine if you have the best plan based on your usage and needs (by solving a system of equations.) etc. I don't know. As a math teacher, I constantly apply what we are doing in classes to teens.... if you want more ways, let me know and I'll pay attention to the things that fall out of my mouth during class when I get "why do we need this?" questions. (because the responses are spontaneous, and without any thought)

I wish my kids could have had you for algebra.

[sigmagirl2000]

I've also taught older HS students how different gambling games have different odds.... and how to calculate them so should they ever visit a casino at some point in their lives, they can maximize winning potential

[southbymidwest]

Originally Posted by MysticCat

He definitely does need to look at it this way, and we hit on this every time we talk about algebra. The challenge is that when you're talking about a 14-year-old with Asperger's, getting him to that macro-perspective is a lot easier said than done.

MC, you are so clever, I am sure that you have tried every which way to get him to understand the importance of algebra on mathematical and non-mathematical levels. But I do find this to be a very interesting and educational discussion, and I am glad that you brought it up.

[mayasophia]

Algebra is needed for construction, such as if you are building a table or laying tile on a new floor. Algebra is needed in all types of projects that require building, that is if you want to do it right.

Algebra is also important if you ever want to get good with money and understanding dividends and interest rates and if you are making a decent return on an investment.

Algebra is also important for programming as well as just basic counting, say if you need to do fractions and split a certain amount of money between multiple people at different rates.

Hope that helps

[MysticCat]

Originally Posted by sigmagirl2000

linear equations can be used in simple applications like "I have to pay my cell phone bill. It costs $50 a month, then $.10 for every text I go over however many are allotted in the plan." The .10 would be your slope, and the $50 would be your y-intercept. You can use those to graph and determine how much you will pay per month based on the number of texts over your plan you use, etc. You can compare your own cell phone plan to other plans to determine if you have the best plan based on your usage and needs (by solving a system of equations.) etc.

How sad is it that I read this three times and still thought "I would have no clue how to do that"?

If it hasn't already been obvious, clearly part of the problem is that our son has two parents for whom math was always something of a foreign language. So, for example, when he was struggling with linear equations, I had to look them up and try to remember/learn again what they are before I could even think of helping him -- I was basically trying to learn them along with him.

Seriously. thanks for the suggestion. Once I wrap my head around it -- and I'll do my best to do that -- I'll try it on him. And yes, I wish he had you for a teacher, too.

[ElieM]

Can you do it backwards? Graphs some points on a graph and then work out the equation that would put them there?

[sigmagirl2000]

Well that was a few sentence explanation of a larger idea. Let's say your monthly plan is $50. You only get 150 texts a month with your plan.

your equation would be y=.10x+50

(x would be number of texts a month over the 150 you get included in plan. y would be the total amount you have to spend)

If you use less than 150 texts in the month, you only pay the $50. So your first point on the graph would be (0,50).

Now let's say you have a super social teenager, and he decides that "texts are pretty cheap!" and uses 1,000 texts in that one month. That's 850 more texts that you get in your plan. Each additional text over your plan costs .10 (I think that's what I used as a random example in previous post). so 850 texts at .10 each comes out to be $85 in texts. (craziness!)

So if you wanted to graph that point, it would be (850, 135) (the 850 is the number of texts beyond what you get. the 135 is the total cost for the month, the $50 monthly charge + the $85 in texts.

If you plot those two points, connect them with a ruler, and you have your line graphed.

Did that make any more sense or just cause more confusion? (it's hard to explain without writing down or speaking)

[sigmagirl2000]

sure. If you have two points (x1, y1) and (x2, y2) just plug them in to m= (y2-y1)/((x2-x1).

That gives you the slope.

Then plug the slope (m) and one of the points you already have into point-slope form of a linear equation:

(y-y1) =m(x-x1)

where m is your slope, y1 is the y-coordinate of one of your points given, and x1 is the x-coordinate of that same point you took y from)

If you feel the need you can simplify to get it in slope-intercept form (y=mx+b), but I personally leave equations in point-slope form and try to get students to do the same.

(yes, I am a nerd. I have a preference for forms of linear equations)

[ElieM]

Sorry, I know you CAN do it backwards, but I was wondering if that would be more interesting for MCs son as it might seem more creative.